Python Program For Recursive Selection Sort For Singly Linked List – Swapping Node Links

Given a singly linked list containing n nodes. The problem is to sort the list using the recursive selection sort technique. The approach should be such that it involves swapping node links instead of swapping node data.  

Examples: 

Input: 10 -> 12 -> 8 -> 4 -> 6
Output: 4 -> 6 -> 8 -> 10 -> 12 

In Selection Sort, we first find the minimum element, swap it with the beginning node and recur for the remaining list. Below is the recursive implementation of these steps for the linked list. 

recurSelectionSort(head)
     if head->next == NULL
         return head
     Initialize min = head
     Initialize beforeMin = NULL
     Initialize ptr = head
    
     while ptr->next != NULL 
         if min->data > ptr->next->data
         min = ptr->next
         beforeMin = ptr
     ptr = ptr->next    
    
     if min != head
         swapNodes(&head, head, min, beforeMin)
    
     head->next = recurSelectionSort(head->next)
     return head

swapNodes(head_ref, currX, currY, prevY)
     head_ref = currY
     prevY->next = currX

     Initialize temp = currY->next
     currY->next = currX->next
     currX->next  = temp    

The swapNodes(head_ref, currX, currY, prevY) is based on the approach discussed here but it has been modified accordingly for the implementation of this post. 

Linked list before sorting:
10 12 8 4 6 
Linked list after sorting:
4 6 8 10 12 

Time Complexity: O(n²), since we are traversing the linked list using a while loop and inside it there is a recursive function is operating at O(n) time thus the complexity turns out to be quadratic
Auxiliary Space: O(n), since we are using recursion all elements in the linked List takes up the entire stack space

Please refer complete article on Recursive selection sort for singly linked list | Swapping node links for more details!